Answer:
Given that,
Random samples of size n = 2 are drawn from a finite population that consists of the numbers 2,4,6, and 8.
(a).
Calculate the mean and the standard deviation of this population:
We have population: 2, 4, 6, 8
Mean ()=(2+4+6+8)/4
=20/4
=5
Standard deviation():
We know that,
(b).
List the six possible random samples of size n = 2 that can be drawn from this population and calculate their means:
Samples are given by:
Samples | Mean |
(2,4) | 3 |
(2,6) | 4 |
(2,8) | 5 |
(4,6) | 5 |
(4,8) | 6 |
(6,8) | 7 |
(c).
Use the results of part (b) to construct the sampling distribution of the mean for random samples of size n =2 from the given population:
Sampling distribution of the mean is:
(d).
Calculate the standard deviation of the sampling distribution obtained in part c) and verify the result by substituting n = 2, N = 4, and the value of σ obtained in part (a):
We know that,
=2.5819/2.2361
=1.1546
For n=2:
=1.4907 (Approximately)
Random samples of size n = 2 are drawn from a finite population that consists of...
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